Thursday, April 06, 2006

Gini's a better measure

The median/mean ratio is problematic for correlating race with income disparity, as it gives more weight to the right side of the income distribution than the left (If Bill Gates' income doubles, the median will stay put but the mean rachet up quite a bit. If Joe pool attendant's income is cut in half, the median will again remain the same, but the mean will only drop slightly). The poverty rate is not an optimal variable either, because it involves only a fraction of the income distribution, has contingencies like family size, varies based on age, and doesn't take into account cost-of-living (poverty rates tend higher in places with a lower cost of living because nominal wages are lower, but this doesn't tell us little about wealth disparities).

Robert at the eponymous Robert's Rationalesuggested use of the Gini coefficient. It scales between 0 and 1, with 0 being perfect income equality and 1 representing a single person with all the income. This eliminates the problem of affluent pull and captures the entire income distribution.

This slightly moderates the strength of the correlations with the significance factor remaining zero. The r-squared for a higher Gini (more income inequality) and the black/Hispanic grouping is .56. For median/mean, it was .58. For non-Hispanic whites/Asians the correlation of lower Gini (more income equality) falls to .43 from .44. While the change is trivial, using Gini provides greater accuracy.

So how should open-border types react? Progressively, of course. They should not look to ten years in the future like those short-sighted conservatives. Instead, they can take the longview--if we accelerate the underclass immigration rate and white birthrates remain below replenishment, in a century the income gap will begin to narrow as the new arrivals are ever-closer to the national average (because it's been falling for the last ninety years)!

3 comments:

Any idea where we could get GINI figures by state by ethnicity? As you've pointed out, ethnicity dominates the differences between the states. I wonder if we'd find anything looking at just white GINI.

Googling for awhile I've only been able to find one or the other. I can probably get a pretty good idea of how stable the gini is likely to be by race across state by looking at gini coefficients by race and taking that to each state, assuming each group within that state has the same as the national gini coefficient and seeing how well it matches up.

Running the proportional difference b/w the actual state gini and the predicted state gini (proportion of each race in a state divided by the four-group total and then multiplied by that group's respective national gini) by race yielded almost identical r-squares for the nhw/asian and blk/hsp groupings. Appears I'm double-measuring something.

But then when I look at the correlation b/w the actual/expected gini and race, the r-square differs for Hispanics and for blacks compared to what it is when correlating state gini by race. The r-square for Hispanics goes up and for blacks goes down, although the two together stay the same. They both correlate with the actual gini being higher than the predicted. So it seems that compared to national disparity, states with more Hispanics push the gini higher than would be predicted by averages, while for blacks the gini is not pushed as high as would be expected by national averages.

Having the race gini by state woule make the picture a lot clearer than approximations.